MODIFICATION OF BOHR MODEL
By Prof. L. Kaliambos ( Natural Philosopher in New Energy) November 26, 2015 INTRODUCTION After my discovery of the dipole nature of photon presented at the international conference "Frontiers of fundamental physics" (1993), today it is well known that according to my discovery of the LAW OF ENERGY AND MASS which rejects Einstein's invalid "mass-energy conservation" in the correct Bohr model the energy ΔE = 13.6 eV of the electron-proton interaction turns to the energy hν = 13.6 eV of the photon in accordance with the conservation law of energy. That is ΔΕ = hν. Moreover accorfing to the conservation law of mass the mass defect ΔΕ/c2 turns to the mass m = hν/c2 of the same photon. Note that Planck in 1907 in order to interpret the gravitational properties of light (predicted by Newton and confirmed by Soldner in 1801) showed that his quanta of energy E = hν do have mass m = hν/c2. Historically, by the middle of the 19th century it was well known that the excited hydrogen gas emitted a distinct emission spectrum. It was noted that the same lines were always present and that the spacing between these lines became smaller and smaller. In 1885, the first person to propose a mathematical relationship for these lines was a Swiss high school teacher, J. J. Balmer. Like Newton (1687) who used Kepler’s empirical law of planetary motion for formulating the universal law of gravitation, in the same way Bohr using the math of Balmer introduced his model of the hydrogen atom. In atomic physics, the Bohr model introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus - similar in structure to the solar system, but with attraction provided by electric forces. In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus. Given this experimental data, Rutherford naturally considered a planetary-model atom, the Rutherford model of 1911 – electrons orbiting a solar nucleus – however, said planetary-model atom has a technical difficulty. The laws of classical mechanics (i.e. the Larmor formula), predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds. This atom model is disastrous, because it predicts that all atoms are unstable. Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster. This would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharges have shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies. To overcome this difficulty, Niels Bohr proposed, in 1913, what is now called the Bohr model of the atom. He suggested that electrons could only have certain classical motions: Electrons in atoms orbit the nucleus. The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits" at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by the Coulomb law. The Bohr model of an atom was based upon Planck's quantum theory of radiation (1900). Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency ν determined by the energy difference of the levels according to the Planck relation: ΔΕ = hν where h is Planck's constant. The significance of the Bohr model is that the laws of electromagnetism apply to the motion of the electron about the nucleus only when restricted by a quantum rule. Although a quantum rule is not completely well defined for small orbits, because the emission process involves two orbits with two different periods, Bohr could determine the energy spacing between levels using the quantum rule and come to an exactly correct quantum rule: the angular momentum L is restricted to be an integer multiple of a fixed unit: L = mυr = nħ where n = 1, 2, 3, ... is called the principal quantum number, and ħ = h/2π. The lowest value of n is 1; this gives a smallest possible orbital radius r = 0.0529 nm known as the Bohr radius. Here m is the mass of electron and υ is the velocity of it. Once an electron is in this lowest orbit,( ground state energy) it can get no closer to the proton. Starting from the angular momentum quantum rule, Bohr was able to calculate the energies of the allowed orbits of the hydrogen atom and other hydrogen-like atoms and ions, like Einstein's incomplete theory of the photoelectric effect,( see my CORRECT EXPLANATION OF PHOTOELECTRIC EFFECT). Under this condition Bohr in his paper “ On the Constitution of Atoms and Molecules” (1913) found that when an electron “falls from infinity” into the ground state energy it loses a total energy ΔΕ which is simply the sum of its kinetic energy mυ2/2 and its potential energy -Ke2/r of the Coulomb law. According to Newton’s second law and to the Coulomb law we can write mυ2/r = Ke2/r2 or mυ2/2 = 0.5Ke2/r So according to the conservation law of energy we get a total negative energy ΔΕ = mυ2/2 - Ke2/r = -0.5Ke2/r = hν Such an energy in terms of eV can be written as ΔΕ = -0.5Ke/r = 13.6 eV = hν THE BOHR MODEL IS MODIFIED BY USING THE SO-CALLED “MASS DEFECT” In my paper " Nuclear structure ..electromagnetism" (2003) I showed in deuteron that the discovery of the so-called “mass defect” gives the photon mass m = hν/c2 in accordance with the conservation law of mass. So, it should be used also in the Bohr model. Today it is well known that according to my discovery of photon mass and of “Matter Matter Interaction” ΔΕ /ΔΜ = hν/m = c2 one sees that during the quantum jump also a mass defect ΔΜ = 13.6 eV/c2 turns into the photon mass m = hν/c2 It means that the simple Bohr model is an incomplete theory which should be modified by using not only the energy ΔΕ but also the mass defect ΔΜ = ΔΕ/c2 . It is of interest to note that the concept of mass defect ΔΜ of the later nuclear reactions at the time of Bohr (1913) was unknown. However It is indeed unfortunate that Einstein believed incorrectly that the mass defect ΔΜ turns into the photon energy hν. Such a fallacious idea did much to retard the progress of atomic and nuclear physics. Fortunately Bohr's condition, that the angular momentum is an integer multiple of ħ was later reinterpreted in 1924 by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit: In 1925 a new kind of mechanics was proposed, quantum mechanics, in which Bohr's model of electrons traveling in quantized orbits was extended into a more accurate model of electron motion. The new theory was proposed by Werner Heisenberg. Another form of the same theory, wave mechanics, was discovered by the Austrian physicist Erwin Schrödinger independently, and by different reasoning. Schrödinger employed de Broglie's matter waves, but sought wave solutions of a three-dimensional wave equation describing electrons that were constrained to move about the nucleus of a hydrogen-like atom, by being trapped by the potential of the positive nuclear charge. Category:Fundamental physics concepts